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Mat. Zametki, 2000, Volume 68, Issue 6, Pages 898–909 (Mi mz1013)  

This article is cited in 1 scientific paper (total in 1 paper)

On Equivalent Normings in the Spaces $H_p^r$ on Compact Homogeneous Spaces

S. S. Platonov

Petrozavodsk State University

Abstract: Let $M$ be an arbitrary compact Riemannian symmetric space of rank 1. The function spaces $H_p^r$ of Nikol'skii type were introduced earlier by means of averaged differences along geodesics. In the present paper we give an equivalent description of these spaces and norms in them by using the Laplace–Beltrami operator. The results obtained generalize the results of Nikol'skii and Lizorkin on the spaces $H_p^r$ over the sphere.

DOI: https://doi.org/10.4213/mzm1013

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English version:
Mathematical Notes, 2000, 68:6, 760–769

Bibliographic databases:

UDC: 517.518
Received: 16.10.1997

Citation: S. S. Platonov, “On Equivalent Normings in the Spaces $H_p^r$ on Compact Homogeneous Spaces”, Mat. Zametki, 68:6 (2000), 898–909; Math. Notes, 68:6 (2000), 760–769

Citation in format AMSBIB
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\paper On Equivalent Normings in the Spaces $H_p^r$ on Compact Homogeneous Spaces
\jour Mat. Zametki
\yr 2000
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\pages 898--909
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\transl
\jour Math. Notes
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\vol 68
\issue 6
\pages 760--769
\crossref{https://doi.org/10.1023/A:1026664801264}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Platonov, “Some problems in the theory of approximation of functions on compact homogeneous manifolds”, Sb. Math., 200:6 (2009), 845–885  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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